Pith Number

pith:WESZU636

pith:2015:WESZU636VZBUKEZ5IMTWOS5F6E

not attested not anchored not stored refs pending

Cohomology for small categories: $k$-graphs and groupoids

Alexander Kumjian, Elizabeth Gillaspy

arxiv:1511.01073 v4 · 2015-11-03 · math.OA · math.CT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WESZU636VZBUKEZ5IMTWOS5F6E}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:10:32.524675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1259a7b7eae4345133d4327674ba5f13589d0beddcf708636a146e1ea506e6b

Aliases

arxiv: 1511.01073 · arxiv_version: 1511.01073v4 · doi: 10.48550/arxiv.1511.01073 · pith_short_12: WESZU636VZBU · pith_short_16: WESZU636VZBUKEZ5 · pith_short_8: WESZU636

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WESZU636VZBUKEZ5IMTWOS5F6E \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b1259a7b7eae4345133d4327674ba5f13589d0beddcf708636a146e1ea506e6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a66616859d551f8e5d1a1d5208c93164deb6b19ac619c6569e52caf8fc098b5",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-11-03T20:35:50Z",
    "title_canon_sha256": "5330a7fb1cfa27a038ca594abed82534a989347c9791a44e3f4855a6b4020fc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01073",
    "kind": "arxiv",
    "version": 4
  }
}